Commutative Ideals of BCI-Algebras Using MBJ-Neutrosophic Structures
As a generalization of a neutrosophic set, the notion of MBJ-neutrosophic sets is introduced by Mohseni Takallo, Borzooei and Jun, and it is applied to BCK/BCI-algebras. In this article, MBJ-neutrosophic set is used to study commutative ideal in BCI-algebras. The concept of closed MBJ-neutrosophic i...
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| Format: | Article |
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/17/2047 |
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| author | Seok-Zun Song Mehmet Ali Öztürk Young-Bae Jun |
| author_facet | Seok-Zun Song Mehmet Ali Öztürk Young-Bae Jun |
| author_sort | Seok-Zun Song |
| collection | DOAJ |
| description | As a generalization of a neutrosophic set, the notion of MBJ-neutrosophic sets is introduced by Mohseni Takallo, Borzooei and Jun, and it is applied to BCK/BCI-algebras. In this article, MBJ-neutrosophic set is used to study commutative ideal in BCI-algebras. The concept of closed MBJ-neutrosophic ideal and commutative MBJ-neutrosophic ideal is introduced and their properties and relationships are studied. The conditions for an MBJ-neutrosophic ideal to be a commutative MBJ-neutrosophic ideal are given. The conditions for an MBJ-neutrosophic ideal to be a closed MBJ-neutrosophic ideal are provided. Characterization of a commutative MBJ-neutrosophic ideal is established. Finally, the extension property for a commutative MBJ-neutrosophic ideal is founded. |
| first_indexed | 2024-03-10T08:08:02Z |
| format | Article |
| id | doaj.art-a700032c10ed45a290a1a77bfdb5c6f4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:08:02Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a700032c10ed45a290a1a77bfdb5c6f42023-11-22T10:57:06ZengMDPI AGMathematics2227-73902021-08-01917204710.3390/math9172047Commutative Ideals of BCI-Algebras Using MBJ-Neutrosophic StructuresSeok-Zun Song0Mehmet Ali Öztürk1Young-Bae Jun2Department of Mathematics, Jeju National University, Jeju 63243, KoreaDepartment of Mathematics, Faculty of Arts and Sciences, Adıyaman University, Adıyaman 02040, TurkeyDepartment of Mathematics Education, Gyeongsang National University, Jinju 52828, KoreaAs a generalization of a neutrosophic set, the notion of MBJ-neutrosophic sets is introduced by Mohseni Takallo, Borzooei and Jun, and it is applied to BCK/BCI-algebras. In this article, MBJ-neutrosophic set is used to study commutative ideal in BCI-algebras. The concept of closed MBJ-neutrosophic ideal and commutative MBJ-neutrosophic ideal is introduced and their properties and relationships are studied. The conditions for an MBJ-neutrosophic ideal to be a commutative MBJ-neutrosophic ideal are given. The conditions for an MBJ-neutrosophic ideal to be a closed MBJ-neutrosophic ideal are provided. Characterization of a commutative MBJ-neutrosophic ideal is established. Finally, the extension property for a commutative MBJ-neutrosophic ideal is founded.https://www.mdpi.com/2227-7390/9/17/2047MBJ-neutrosophic setMBJ-neutrosophic subalgebraMBJ-neutrosophic idealcommutative MBJ-neutrosophic ideal |
| spellingShingle | Seok-Zun Song Mehmet Ali Öztürk Young-Bae Jun Commutative Ideals of BCI-Algebras Using MBJ-Neutrosophic Structures Mathematics MBJ-neutrosophic set MBJ-neutrosophic subalgebra MBJ-neutrosophic ideal commutative MBJ-neutrosophic ideal |
| title | Commutative Ideals of BCI-Algebras Using MBJ-Neutrosophic Structures |
| title_full | Commutative Ideals of BCI-Algebras Using MBJ-Neutrosophic Structures |
| title_fullStr | Commutative Ideals of BCI-Algebras Using MBJ-Neutrosophic Structures |
| title_full_unstemmed | Commutative Ideals of BCI-Algebras Using MBJ-Neutrosophic Structures |
| title_short | Commutative Ideals of BCI-Algebras Using MBJ-Neutrosophic Structures |
| title_sort | commutative ideals of bci algebras using mbj neutrosophic structures |
| topic | MBJ-neutrosophic set MBJ-neutrosophic subalgebra MBJ-neutrosophic ideal commutative MBJ-neutrosophic ideal |
| url | https://www.mdpi.com/2227-7390/9/17/2047 |
| work_keys_str_mv | AT seokzunsong commutativeidealsofbcialgebrasusingmbjneutrosophicstructures AT mehmetaliozturk commutativeidealsofbcialgebrasusingmbjneutrosophicstructures AT youngbaejun commutativeidealsofbcialgebrasusingmbjneutrosophicstructures |